Question

If the $7^{th}$ term of a harmonic progression is 8 and the $8^{th}$ term is 7, then its ${15}^{th}$ term is

• A. 16
• B. 14
• C. $\frac{27}{14}$
• D. $\frac{56}{15}$

Answer 1

The correct option is D

$\frac{56}{15}$

Obviously, $7^{th}$ term of corresponding A.P is $\frac{1}{8}$ and $8^{th}$

term will be $\frac{1}{7}$. a + 6d = $\frac{1}{8}$ and a+7d = $\frac{1}{7}$

Solving these, we get d = $\frac{1}{56}$ and a = $\frac{1}{56}$

Therefore ${15}^{th}$ term of this A.P.

= $\frac{1}{56}+14\times \frac{1}{56}$ = $\frac{15}{56}$

Hence the required ${15}^{th}$ term of the H.P. is $\frac{56}{15}$